Probing Lorentz Invariance Violation with Neutrino Factories

In this article we show the modification in the number of neutrino events ($\nu_\mu+\bar\nu_\mu$) caused by Lorentz Invariant Violation (LIV), $\sigma=5\times 10^{-24}$ and $10^{-23}$, in neutrino oscillation for a neutrino factory at a distance of 7500 km. The momentum of the muons can vary from 10-50 GeV and we consider $2\times 10^{20}$ decays per year. The modifications in the number of events caused by this $\sigma$ LIV parameter could be a strong signal of new physics in a future neutrino factory.Comment: 8 pages, 6 figures. Several improvements in the text. New references added. Improvements in the discussions and conclusion

Weak Conservation Laws for Minimizers which are not Pontryagin Extremals

We prove a Noether-type symmetry theorem for invariant optimal control problems with unrestricted controls. The result establishes weak conservation laws along all the minimizers of the problems, including those minimizers which do not satisfy the Pontryagin Maximum Principle.Comment: Accepted for presentation (Paper No: 113) at the 2nd International Conference "Physics and Control" (PhysCon 2005), August 24-26, 2005, Saint Petersburg, Russia. To appear in the respective Conference Proceeding